tol=1e-12; SEQ_main_ACCURACY(tol)

====================================================================================

               >>>   Example 5 - Talbot Suite DE   <<<

         Application of Talbot's method to solve the PDE equation

			u_t (x,y,t) = u_xx (x,y,t) + u_yy (x,y,t),      0 < x,y < 1,  t>0

	with conditions:
			u(x,y,0+) = x*(x-1) + y*(y-1)
			u(0,y,t) = u(1,y,t) = 4*t + y*(y-1)
			u(x,0,t) = u(x,1,t) = 4*t + x*(x-1)

	The analytical solution is

		u(x,y,t) = 4*t + x*(x-1) + y*(y-1)

	and its Laplace Transform is

		            4    x*(x-1) + y*(y-1)
		U(x,y,s) = --- + -----------------
		           s^2           s

	with a double pole at 0

	     and abscissa of convergence: sigma0 = 0

====================================================================================

	   Ex. 5: output from ./1SEQ/LTS3_mex_Cmain/SEQ_main_ACCURACY.c
	LT samples by solving in MATLAB block tridiagonal systems

	      5 t in [100, 500],    9 x,y in [0, 1],    tol=1.000000e-12
====================================================================================


RELERR1 = [ %  Tval(1)    Tval(2)    ...    Tval(5)
 1          1.285435e-11  2.700801e-15  1.137076e-15  2.984688e-15  1.102883e-14    % XYval( 1)
 2          1.286341e-11  2.701065e-15  1.705725e-15  5.401127e-15  1.421296e-14    % XYval( 2)
 3          1.286890e-11  3.269902e-15  2.274388e-15  8.812623e-15  2.342351e-14    % XYval( 3)
 4          1.287082e-11  2.985621e-15  2.084883e-15  7.107024e-15  1.603272e-14    % XYval( 4)
 5          1.286890e-11  3.269902e-15  3.032518e-15  7.817650e-15  1.728337e-14    % XYval( 5)
 6          1.286341e-11  2.701065e-15  1.705725e-15  7.106746e-15  1.694185e-14    % XYval( 6)
 7          1.285435e-11  2.700801e-15  2.084639e-15  3.837455e-15  1.364391e-14    % XYval( 7)
 8          1.286341e-11  2.701065e-15  1.705725e-15  5.401127e-15  1.773778e-14    % XYval( 8)
 9          1.287275e-11  3.838730e-15  3.032597e-15  9.523505e-15  2.365130e-14    % XYval( 9)
10          1.287895e-11  3.412405e-15  3.222260e-15  1.066095e-14  3.229387e-14    % XYval(10)
11          1.288031e-11  3.696844e-15  3.222302e-15  1.151394e-14  3.320382e-14    % XYval(11)
12          1.287895e-11  3.412405e-15  3.222260e-15  1.151383e-14  2.967852e-14    % XYval(12)
13          1.287275e-11  3.838730e-15  3.032597e-15  8.528512e-15  2.365130e-14    % XYval(13)
14          1.286341e-11  2.701065e-15  1.705725e-15  6.253936e-15  1.773778e-14    % XYval(14)
15          1.286890e-11  3.269902e-15  2.274388e-15  8.812623e-15  2.524282e-14    % XYval(15)
16          1.287895e-11  3.412405e-15  3.222260e-15  1.066095e-14  3.490922e-14    % XYval(16)
17          1.288416e-11  4.123564e-15  3.980594e-15  1.236707e-14  3.616089e-14    % XYval(17)
18          1.288609e-11  3.554866e-15  3.980646e-15  1.051922e-14  3.274974e-14    % XYval(18)
19          1.288416e-11  4.123564e-15  3.980594e-15  1.151417e-14  3.263577e-14    % XYval(19)
20          1.287895e-11  4.265506e-15  3.222260e-15  9.808076e-15  3.047450e-14    % XYval(20)
21          1.286890e-11  3.269902e-15  2.274388e-15  6.964815e-15  2.524282e-14    % XYval(21)
22          1.287082e-11  2.985621e-15  2.084883e-15  8.102007e-15  1.967136e-14    % XYval(22)
23          1.288031e-11  3.696844e-15  3.222302e-15  1.066106e-14  3.229413e-14    % XYval(23)
24          1.288609e-11  3.554866e-15  3.980646e-15  1.322010e-14  3.900403e-14    % XYval(24)
25          1.288816e-11  3.554936e-15  4.170255e-15  1.194085e-14  3.752604e-14    % XYval(25)
26          1.288609e-11  3.554866e-15  3.980646e-15  9.524156e-15  2.831488e-14    % XYval(26)
27          1.288031e-11  2.843726e-15  3.222302e-15  8.813140e-15  2.706339e-14    % XYval(27)
28          1.287082e-11  2.985621e-15  2.084883e-15  5.401338e-15  1.967136e-14    % XYval(28)
29          1.286890e-11  3.269902e-15  2.274388e-15  6.964815e-15  2.171792e-14    % XYval(29)
30          1.287895e-11  3.412405e-15  3.222260e-15  9.808076e-15  2.694947e-14    % XYval(30)
31          1.288416e-11  4.123564e-15  3.980594e-15  1.236707e-14  3.263577e-14    % XYval(31)
32          1.288609e-11  3.554866e-15  3.980646e-15  1.051922e-14  3.093031e-14    % XYval(32)
33          1.288416e-11  4.123564e-15  3.980594e-15  1.151417e-14  3.081636e-14    % XYval(33)
34          1.287895e-11  3.412405e-15  3.222260e-15  1.066095e-14  2.865513e-14    % XYval(34)
35          1.286890e-11  3.269902e-15  1.326726e-15  6.964815e-15  2.262757e-14    % XYval(35)
36          1.286341e-11  2.701065e-15  1.705725e-15  5.401127e-15  1.421296e-14    % XYval(36)
37          1.287275e-11  3.838730e-15  3.032597e-15  7.675661e-15  2.365130e-14    % XYval(37)
38          1.287895e-11  3.412405e-15  3.222260e-15  1.066095e-14  3.320356e-14    % XYval(38)
39          1.288031e-11  3.696844e-15  3.222302e-15  9.808172e-15  2.706339e-14    % XYval(39)
40          1.287895e-11  3.412405e-15  3.222260e-15  9.808076e-15  2.865513e-14    % XYval(40)
41          1.287275e-11  3.838730e-15  3.032597e-15  8.528512e-15  2.274163e-14    % XYval(41)
42          1.286341e-11  2.701065e-15  1.705725e-15  5.401127e-15  1.421296e-14    % XYval(42)
43          1.285435e-11  2.700801e-15  1.137076e-15  3.837455e-15  1.011924e-14    % XYval(43)
44          1.286341e-11  2.701065e-15  1.705725e-15  5.401127e-15  1.694185e-14    % XYval(44)
45          1.286890e-11  3.269902e-15  1.326726e-15  6.964815e-15  2.342351e-14    % XYval(45)
46          1.287154e-11  2.985621e-15  2.084883e-15  7.107024e-15  2.046731e-14    % XYval(46)
47          1.286890e-11  3.269902e-15  2.274388e-15  6.111981e-15  2.171792e-14    % XYval(47)
48          1.286341e-11  2.701065e-15  1.705725e-15  6.253936e-15  1.955704e-14    % XYval(48)
49          1.285435e-11  2.700801e-15  1.137076e-15  4.832351e-15  1.455351e-14    % XYval(49)
          ];

RELERR2 = [ %  Tval(1)    Tval(2)    ...    Tval(5)
 1          5.687452e-16  8.528845e-16  3.790252e-16  2.842560e-16  5.684964e-16    % XYval( 1)
 2          1.422141e-16  1.705936e-15  1.895250e-16  8.528095e-16  1.705556e-15    % XYval( 2)
 3          1.137846e-15  1.990375e-15  3.790647e-16  7.106954e-16  1.364477e-15    % XYval( 3)
 4          1.137891e-15  1.421724e-15  5.686045e-16  8.528428e-16  1.705609e-15    % XYval( 4)
 5          1.137846e-15  1.279527e-15  3.790647e-16  7.106954e-16  1.364477e-15    % XYval( 5)
 6          8.532846e-16  1.705936e-15  1.895250e-16  1.705619e-15  7.959260e-16    % XYval( 6)
 7          2.843726e-16  8.528845e-16  3.790252e-16  2.842560e-16  1.364391e-15    % XYval( 7)
 8          8.532846e-16  1.705936e-15  7.580998e-16  1.705619e-15  1.705556e-15    % XYval( 8)
 9          2.844838e-16  2.416978e-15  3.790746e-16  1.421419e-15  1.250790e-15    % XYval( 9)
10          2.845172e-16  2.843671e-15  3.790894e-16  9.950222e-16  1.478241e-15    % XYval(10)
11          8.535849e-16  3.270285e-15  3.790943e-16  8.528845e-16  1.478252e-15    % XYval(11)
12          1.280327e-15  2.843671e-15  3.790894e-16  1.705752e-15  1.478241e-15    % XYval(12)
13          2.844838e-16  2.416978e-15  5.686119e-16  1.421419e-15  1.250790e-15    % XYval(13)
14          8.532846e-16  7.108065e-16  7.580998e-16  1.705619e-15  1.705556e-15    % XYval(14)
15          1.137846e-15  1.990375e-15  3.790647e-16  7.106954e-16  1.364477e-15    % XYval(15)
16          5.690343e-16  2.843671e-15  3.790894e-16  1.705752e-15  1.478241e-15    % XYval(16)
17          2.845506e-16  3.839180e-15  3.791042e-16  1.705802e-15  2.046843e-15    % XYval(17)
18          2.845617e-16  3.554866e-15  5.686637e-16  2.558728e-15  1.933144e-15    % XYval(18)
19          2.845506e-16  3.839180e-15  5.686563e-16  2.700854e-15  2.046843e-15    % XYval(19)
20          5.690343e-16  2.843671e-15  3.790894e-16  1.705752e-15  1.478241e-15    % XYval(20)
21          1.137846e-15  1.279527e-15  3.790647e-16  1.705669e-15  1.364477e-15    % XYval(21)
22          1.137891e-15  2.274759e-15  3.790696e-16  1.847826e-15  1.705609e-15    % XYval(22)
23          1.422641e-16  2.417167e-15  3.790943e-16  1.705769e-15  1.478252e-15    % XYval(23)
24          2.845617e-16  3.554866e-15  5.686637e-16  1.705819e-15  1.933144e-15    % XYval(24)
25          8.537184e-16  3.412738e-15  1.137342e-15  2.132295e-15  1.592014e-15    % XYval(25)
26          5.691234e-16  2.701698e-15  1.516437e-15  2.558728e-15  1.933144e-15    % XYval(26)
27          1.422641e-16  2.417167e-15  3.790943e-16  1.705769e-15  2.274234e-15    % XYval(27)
28          1.137891e-15  1.421724e-15  5.686045e-16  1.847826e-15  1.705609e-15    % XYval(28)
29          1.422308e-16  1.990375e-15  3.790647e-16  1.705669e-15  1.364477e-15    % XYval(29)
30          2.845172e-16  3.696772e-15  3.790894e-16  1.705752e-15  1.478241e-15    % XYval(30)
31          2.845506e-16  3.839180e-15  5.686563e-16  1.705802e-15  2.046843e-15    % XYval(31)
32          2.845617e-16  3.554866e-15  5.686637e-16  1.705819e-15  1.933144e-15    % XYval(32)
33          2.845506e-16  2.986029e-15  5.686563e-16  1.705802e-15  2.046843e-15    % XYval(33)
34          5.690343e-16  2.843671e-15  3.790894e-16  1.705752e-15  1.478241e-15    % XYval(34)
35          1.422308e-16  1.990375e-15  3.790647e-16  7.106954e-16  1.364477e-15    % XYval(35)
36          1.422141e-16  1.705936e-15  1.895250e-16  1.705619e-15  1.705556e-15    % XYval(36)
37          2.844838e-16  2.416978e-15  5.686119e-16  1.421419e-15  1.250790e-15    % XYval(37)
38          2.845172e-16  2.843671e-15  3.790894e-16  1.705752e-15  5.685541e-16    % XYval(38)
39          1.422641e-16  2.417167e-15  3.790943e-16  1.705769e-15  5.685586e-16    % XYval(39)
40          5.690343e-16  2.843671e-15  1.137268e-15  1.705752e-15  1.478241e-15    % XYval(40)
41          2.844838e-16  2.416978e-15  5.686119e-16  1.421419e-15  1.250790e-15    % XYval(41)
42          1.422141e-16  1.705936e-15  1.895250e-16  1.705619e-15  7.959260e-16    % XYval(42)
43          5.687452e-16  8.528845e-16  3.790252e-16  2.842560e-16  1.364391e-15    % XYval(43)
44          8.532846e-16  1.705936e-15  1.895250e-16  8.528095e-16  1.705556e-15    % XYval(44)
45          1.137846e-15  1.990375e-15  3.790647e-16  7.106954e-16  4.548255e-16    % XYval(45)
46          1.137891e-15  1.421724e-15  5.686045e-16  8.528428e-16  1.705609e-15    % XYval(46)
47          1.422308e-16  1.279527e-15  3.790647e-16  1.705669e-15  4.548255e-16    % XYval(47)
48          1.422141e-16  1.705936e-15  1.895250e-16  1.705619e-15  1.705556e-15    % XYval(48)
49          2.843726e-16  8.528845e-16  3.790252e-16  2.842560e-16  1.364391e-15    % XYval(49)
          ];
diary off
